pts=Flatten[Table[{{x,y},Hue[Random[]]},{x,-1,1,0.25},{y,-1,1,0.25}],1];

StreamPlot[{-y^2,Sin[x]},{x,-1,1},{y,-1,1},AspectRatio->Automatic,StreamPoints->{pts,Automatic,Scaled[2.3]},StreamScale->None,Epilog->{Blue,PointSize[Medium],Point[pts[[All,1]]]}]